Question

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Answer 1

1. 1) $\frac{8x^{5}y^{6} }{12x^{4}y^{7} } =\frac{2x^{5}y^{6} }{3x^{4}y^{7} } =\frac{2xy^{6} }{3y^{7} }=\frac{2x}{3y}$

  2) $\frac{(c-d)^{2} }{c^{2}-d^{2} } =\frac{(c-d)^{2} }{(c+d)(c-d)} =\frac{c-d}{c+d}$

  3) $\frac{5a-15b}{a^{2}-9b^{2} } =\frac{5(a-3b)}{a^{2}-9b^{2} } =\frac{5(a-3b)}{(a+3b)(a-3b)}=\frac{5}{a+3b}$

2. 1) $\frac{3y-2x}{x+y}-\frac{2y-3x}{x+y} =\frac{3y-2x-2y+3x}{x+y}=1$

   2)$\frac{3a}{4b} +\frac{9a}{4b} =\frac{3a+9a}{4b} =\frac{12a}{4b}=\frac{3a}{b}$

  3) $\frac{h^{2} }{h+g} -\frac{g^{2} }{h+g} =\frac{h^{2}-g^{2} }{h+g } =\frac{(h+g)(h-g)}{h+g} =h-g$

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